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                                                                     EXHIBIT 5.1

                                 Credit Suisse First Boston Corporation
                                 Salomon Smith Barney, Inc.
                                 Deutsche Bank Alex Brown
                                 CIBC World Markets Corp.
                                 Dain Rauscher Incorporated
                                 Morgan Keegan & Company, Inc.,
                                 as representatives of the several underwriters,
                                 c/o Credit Suisse First Boston Corporation
                                 Eleven Madison Avenue
                                 NEW YORK, NY 10010-3629
                                 United States of America


                                 Rotterdam, 23 May 2000


                                 Chris Fonteijn, advocaat
                                 telephone      : +031 10 224 03 71
                                 fax            : +031 10 224 00 57
                                 e-mail         : fonteic@nautadutilh.nl

Dear Sirs,

We have acted as Netherlands legal counsel to Core Laboratories N.V., a public
company with limited liability incorporated under the laws of the Netherlands
("the Company"), in connection with the registration statement on Form S-3
(Registration No. 333-36042) filed by the Company with the Securi-

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ties and Exchange Commission ("the Commission") on 1st May 2000 ("the
Registration Statement"), as amended by Amendment No. 1 filed on 23 May 2000, in
connection with the registration under the Securities Act of 1933, as amended,
of 5,504,105 common shares in the capital of the Company ("Common Shares").

For the purpose of rendering this opinion we have examined and relied only on
the following documents:

(a)    a faxed copy of the Registration Statement;

(b)    a faxed copy of a draft of Amendment No. 1 to the Registration Statement;

(c)    a faxed copy of the prospectus included in such Registration Statement
       ("the Prospectus"); and

(d)    copies of the following documents in relation to the Company:

       1.  a photocopy of the deed of incorporation of the Company as a private
           company with limited liability under Netherlands law ("besloten
           vennootschap met beperkte aansprakelijkheid") under the name of Core
           Holdings B.V. with its corporate seat at Amsterdam, the Netherlands,
           dated 8 August 1994, incorporating the articles of association
           ("statuten") of the Company;

       2.  a photocopy of a notarial deed dated 31 August 1995, providing for
           the conversion of the Company (following such conversion known as
           "Core Laboratories N.V.") into a public company with limited
           liability ("naamloze vennootschap");

       3.  a photocopy of a notarial deed dated 2 July 1998, providing for the
           amendment of the articles of association of the Company with a copy
           of the latest articles of association of the Company;
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       4.  a faxed copy of the resolution of the Board of Supervisory Directors
           of the Company dated 10 December 1999 authorizing, inter alia, the
           issue of 627,930 shares for the acquisition of TomoSeis Corporation
           with a faxed copy of the certificate of the Company's secretary dated
           7 January 2000 certifying that the aforementioned copy is a true,
           accurate and complete copy of the resolutions adopted by the
           Supervisory Board on 10 December 1999;

       5.  a faxed copy of the resolution of the Board of Supervisory Directors
           of the Company dated 6 May 1999 authorizing, inter alia, the
           issue of up to 300,000 shares for the acquisition of Reservoirs, Inc.
           with a faxed copy of the certificate of the Company's secretary dated
           26 July 1999 certifying that the aforementioned copy is a true,
           accurate and complete copy of the resolutions adopted by the
           Supervisory Board on 6 May 1999;

       6.  a faxed copy of a draft of a resolution of the Board of Supervisory
           Directors of the Company authorizing, inter alia, the option to issue
           up to 750,000 additional shares to certain underwriters;

the documents referred to in (a) (b) and (c) above are hereinafter referred to
as: "the Documents" and the documents referred to in paragraph (d) above as "the
Certificates".

In rendering this opinion, we have assumed that:

(i)        the genuineness of all signatures to all Documents and Certificates,
           the completeness and the conformity to the original documents of all
           Documents and Certificates submitted to us as faxed copies or
           photocopies and the authenticity of such original documents;

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(ii)       the accuracy, validity and binding effect of the Documents and the
           matters certified or evidenced thereby under any applicable law other
           than Netherlands law;

(iii)      the resolutions referred to in items 4 and 5 above under c are in
           full force and effect and are adopted without any change and the
           resolution referred to in item 6 above under d will be executed,
           substantially in the form of the draft referred to above;

(iv)       the statements as mentioned in Article 2:94b Dutch Civil Code with
           respect to the contribution in kind for the acquisition of TomoSeis
           Corporation and Reservoirs Inc. as referred to in items 4 and 5
           above under d will be issued.

This opinion shall be governed by and construed and have effect in accordance
with Netherlands law and is given only with respect to Netherlands law in effect
on the date of this opinion. We have not investigated the laws of any
jurisdiction other than the Netherlands, any matters of fact, tax law,
anti-trust law or international law, including, without limitation, the law of
the European Community. Any liability of our firm, its members and its employees
in connection with this opinion shall be limited to the amount which is paid out
in the matter concerned under our firms professional liability policies.

Based on and subject to the foregoing and subject to the qualifications set
forth below, we express the following opinion:

         The shares in the capital of the Company to be issued by the Company or
         sold by the selling shareholders referred to in the Registration
         Statement, as reflected in the


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         Registration Statement, consisting of a maximum of 5,504,105 common
         shares, when issued by the Company or sold by the said selling
         shareholders, as applicable, in the manner and on the terms as referred
         to in the Registration Statement and the Prospectus, will be duly and
         validly issued and, subject to payment for such shares issued by the
         Company, such shares will be fully paid and non-assessable.

The opinion expressed above is subject to the following qualification:

         We have assumed that any foreign law which may apply with respect to
         the Documents or the transactions contemplated thereby would not be
         such as to affect the opinion expressed herein.

This opinion is addressed to you. It may not be relied upon by any other person
or company and without our prior written consent its contents may not be
disclosed, save to your legal advisors who may rely upon this opinion as though
it were addressed to them. We consent to the inclusive of this opinion as an
exhibit to the Registration Statement. We further consent to all references to
us in the Registration Statement, the Prospectus and any amendments or
supplements thereto.




                                    Yours sincerely,

                                    NAUTA DUTILH

                                    /s/ CHRIS A. FONTEIJN
                                    --------------------------------------------
                                        Chris A. Fonteijn,
                                        advocaat